I was wondering if someone could please suggest a technique for solving the following system of ODEs:
$$x_1'=(1+2\cos2t)x_1 + (1-2\sin2t)x_2$$
$$x_2'=-(1+2\sin2t)x_1 + (1-2\cos2t)x_2$$
What I initially tried to do was differentiate the first equation to obtain an equation for $x_1''$ and then substitute expressions for $x_2$ and $x_2'$. This resulted in a second-order DE involving $x_1''$, $x_1'$, and $x_1$. But this equation was extremely complex in terms of its variable coefficients. I am thinking there must be a simpler approach. Thanks.